In a typical controller, the control gains \(k=[k_s, k_v, k_a]\) , time gap setting \(\tau ^*\) , and parameters \(T_L\)  and \(K_L\)  are preset for each vehicle. However, parameters \(T_L\)  and \(K_L\)  are stochastic in nature, and there is no guarantee that they remain consistent in real-life conditions. For instance, the recent empirical analysis on commercial ACC-enabled vehicles by [1]} estimated systematic delays in system sensors to be \(0.1-1\)  seconds. Note that these delays are related to second-order lags (i.e., pertaining to speed and location), whereas \(T_L\)  and \(K_L\)  are related to third-order lags. While the estimates of second-order lags are not strictly equivalent to \(T_L\)  or \(K_L\) , they suggest the significant impact of these parameters and variation in experienced delays by real-life vehicles. [2]} shows the impact of different actuation lag values on the acceleration profile of the vehicle controller and its overall stability.
